Try contacting Dr Sautov and hopefully he will respond, but if you don't get anywhere that way, I would still suggest contacting Olga Filimonova, and she can pass things on to him, hopefully.
I am not sure if they actually have some fund for cash donations from abroad, but I was told that there is a group of Americans and British, who regularly purchase antique items at auctions, items that either once belonged to the palace (both CP and AP I believe) or things that are analogous, fromt the same period, area or maker, etc. These people then donate these things to the museum. This group is called "Friends of TS Museum" or something to that effect, and they come there every year and are given a reception and shown around.
I think that it is a lot more complicated with cash donations, and this is why they tend to do it this way. But I can try to reconfirm if there is some sort of a fund that accepts cash donations for the AP.